Twisted Edwards Curves
By Daniel J. Bernstein, Peter Birkner, Marc Joye, Tanja Lange, C. Peters. International Conference on Cryptology in Africa, 2008
486 citations recorded by the source corpus.
This paper introduces "twisted Edwards curves," a generalization of the recently introduced Edwards curves; shows that twisted Edwards curves include more curves over finite fields, and in particular every elliptic curve in Montgomery form; shows how to cover even more curves via isogenies; presents fast explicit formulas for twisted Edwards curves in projective and inverted coordinates; and shows that twisted Edwards curves save time for many curves that were already expressible as Edwards curves.
Subfields: Computational Mechanics, Geometry and Topology, Information Systems
View Paper: https://www.semanticscholar.org/paper/6bd787497fb26ba4633f1e0ffc06d9b814234e6a
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In Computational Mechanics
In Geometry and Topology
In Information Systems
- Peter Schwabe
- Tanja Lange
- Bo-Yin Yang
- Niels Duif
- Daniel J. Bernstein
- George Danezis
- Ethan Buchman
- Michael Naehrig
Citations in the corpus
- High-speed high-security signatures (2011, methodology): “…below; and an element B (cid:4)= ( 0 , 1 ) of the set The condition that d is not a square implies that d (cid:4)∈ { 0 , − 1 } , so this set E forms a group with neutral element 0 = ( 0 , 1 ) under the twisted Edwards addition law introduced by Bernstein, Birkner, Joye, Lange, and Peters in [13].”
- Towards quantum-resistant cryptosystems from supersingular elliptic curve isogenies (2011, background): “Consequently, it is isomorphic to a twisted Edwards curve and to a Montgomery curve [3].”